"Twitter is hard to evaluate. They have a lot of potential. It's a horribly mismanaged company—probably a lot of pot-smoking going on there. But it's such a solid franchise it may even work with all that," the co-founder of PayPal and early Facebook investor said in a "Squawk Box" interview.

But Thiel said he would not call for the ouster of Twitter CEO Dick Costolo. "I'm not sure they could do that much better. The CEO can't really change things that much in these companies. You'd have to fire everybody and start over."